Answer:
the amount of force needed to hold the nozzle is 1100 N
Explanation:
Given that;
The diameter of the fire horse is 7.0cm
The radius of the fire horse is d/2 = 7.0/2 = 3.5 cm = 0.035 m
the water running through the hose flows at 420 L/min = 0.42 m³/ 60 sec
The diameter of the nozzle = 0.75 cm
The radius of the nozzle = d/2 = 0.75/2 = 0.375 cm = 0.00375 m
Amount of force needed to hold the nozzle = ??
Using equation of continuity product
where
= cross sectional area of the hose
= velocity of water flow at hose
= cross sectional area of the nozzle
= velocity of water flow at nozzle
Making the subject of the formula; we have
Also making the subject of the formula:
Also; from newton's law; we all know that F = ma
where ;
m = mass
a = acceleration
So ;
Also ; mass = density × volume
Replacing by from above ; so
where the product of cross section area of velocity is equal to the volume of water and its time flow;
SO;
Replacing that into what we have above; we have:
Where;
A = πr²
F = 1100 N
Thus; the amount of force needed to hold the nozzle is 1100 N